Abstract: Power saving is an important issue for mobile handsets since they must rely on their batteries. To reduce the battery consumption of mobile handsets, we propose a fractional threshold-based wake-up mechanism, which switches the system into the sleep mode when the packet-receiving queue is empty, and switches the system on when the number of packets in the queue "reaches" a fractional threshold value. A fractional threshold value can be any real number, instead of just a natural number. In fact, the fractional threshold value indicates the mean threshold value. Our study indicates that the fractional threshold scheme with probability 1 provides an optimal power saving solution. The optimization objective is to minimize switch-on rate while satisfying the Quality of Service requirement, which is an upper bound of packet dropping probability.